| Description |
1 online resource (x, 305 pages) : illustrations |
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text txt rdacontent |
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computer c rdamedia |
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online resource cr rdacarrier |
| Series |
Studies in mathematics and its applications ; v. 33 |
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Studies in mathematics and its applications ; v. 33.
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| Summary |
Recent decades have seen a very rapid success in developing numerical methods based on explicit control over approximation errors. It may be said that nowadays a new direction is forming in numerical analysis, the main goal of which is to develop methods ofreliable computations. In general, a reliable numerical method must solve two basic problems: (a) generate a sequence of approximations that converges to a solution and (b) verify the accuracy of these approximations. A computer code for such a method must consist of two respective blocks: solver and checker. In this book, we are chiefly concerned with the problem (b) and try to present the main approaches developed for a posteriori error estimation in various problems. The authors try to retain a rigorous mathematical style, however, proofs are constructive whenever possible and additional mathematical knowledge is presented when necessary. The book contains a number of new mathematical results and lists a posteriori error estimation methods that have been developed in the very recent time. computable bounds of approximation errors checking algorithms iteration processes finite element methods elliptic type problems nonlinear variational problems variational inequalities. |
| Contents |
Contents -- 1. Introduction. -- 2. Mathematical background. -- 3. A posteriori estimates for iteration methods. -- 4. A posteriori estimates for finite element approximations. -- 5. Foundations of duality theory. -- 6. Two-sided a posteriori estimates for linear elliptic problems. -- 7. A posteriori estimates for nonlinear variational problems. -- 8. A posteriori estimates for variational inequalities. -- Bibliography. -- Notation. -- Index. |
| Bibliography |
Includes bibliographical references (pages 281-299) and index. |
| Note |
Print version record. |
| Language |
English. |
| Subject |
Numerical analysis.
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Error-correcting codes (Information theory)
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Approximation theory.
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Analyse numérique.
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Codes correcteurs d'erreurs (Théorie de l'information)
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Théorie de l'approximation.
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COMPUTERS -- Computer Simulation.
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Approximation theory
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Error-correcting codes (Information theory)
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Numerical analysis
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| Added Author |
Repin, Sergey I.
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| Other Form: |
Print version: Neittaanmäki, P. (Pekka). Reliable methods for computer simulation. Amsterdam ; San Diego, CA : Elsevier, 2004 0444513760 9780444513762 (DLC) 2006277839 (OCoLC)56463686 |
| ISBN |
9780444513762 |
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0444513760 |
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9781435601017 (electronic bk.) |
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1435601017 (electronic bk.) |
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0080540503 |
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9780080540504 |
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1281019089 |
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9781281019080 |
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9786611019082 |
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6611019081 |
| Standard No. |
AU@ 000048131141 |
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AU@ 000062577132 |
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CHNEW 001005558 |
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DEBBG BV036962228 |
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DEBBG BV042317245 |
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DEBSZ 276904303 |
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DEBSZ 482351268 |
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NZ1 12432693 |
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NZ1 15192825 |
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